ELECTRICAL BREAKDOWN OF GASES IN …

ELECTRICAL BREAKDOWN OF GASES IN SUBATOMOSPHERIC PRESSURE

by

Yuxuan Chen

A thesis submitted to the Graduate Faculty of

Auburn University

in partial fulfillment of the

requirements for the Degree of

Master of Science

Auburn, Alabama

August 6, 2016

Copyright 2016 by Yuxuan Chen

Approved by

Hulya Kirkici, Chair, Professor of Electrical and Computer Engineering

Thaddeus Roppel, Member, Associate Professor of Electrical and Computer Engineering

Shiwen Mao, Member, Professor of Electrical and Computer Engineering

ii

Abstract

In this study, I present my research on the breakdown phenomenon and discharge

characteristics of gaseous dielectrics under DC voltages with different pressures. All of the

experiments conducted utilized a point-to-point stainless steel electrode pair separated at 1cm

gap distance. The theoretical and experimental breakdown voltage results of different gases are

compared. It is observed that different gases has different breakdown voltage under the same

experimental conditions and electrode geometry. Besides, the breakdown voltage versus

pressure curves of gaseous dielectrics follows the classic Paschen’s Law as well. In conclusion,

it is shown that the theoretical calculation values are correct. The air and nitrogen have the

better insulating properties at selected 1 Torr to 2 Torr range, compared to other gases used in

this study.

iii

Acknowledgement

I am grateful to my advisor Dr. Hulya Kirkici for her patience and guidance. The door to

Prof. Kirkici’s office was always open whenever I ran into a trouble spot or had a question

about my research. I would like to thank Dr. Mao and Dr. Roppel for serving as the committee

members.

The graduate peers I would like to thank are Dr. Alper Kara, Mike Moley, and Baha

Yakupoglu, for their help during the months of research dedicated to troubleshooting with the

experiment setup over and over again.

I am truly grateful for the enormous support from my parents. With their encouragement

and help, I eventually finished my thesis and degree.

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Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ii

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ⅵ

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ⅶ

Chapter 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Chapter 2 BACKGROUND AND LITERATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

2.1 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

2.2 Gas Breakdown mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

2.2.1 Townsend discharge theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

2.2.2 Paschen’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

2.2.3 Streamer Theory of Breakdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

2.3 High Frequency Breakdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

2.4 Air and Gas dielectrics Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

2.4.1 Air Insulation Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

2.4.2 Gas Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

2.4.3 Vacuum Surface Flashover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

2.5 Space System Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Chapter 3 EXPERIMENTAL SETUP AND PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . .19

3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

3.2 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

Chapter 4 RESULTS AND DISCUSSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

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4.1 Theoretical Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

4.2 DC Breakdown Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

4.3 Comparison between Theoretical and Experimental Curves . . . . . . . . . . . . . . . . .34

4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38

Chapter 5 RESULTS AND DISCUSSION. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 39

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41

vi

List of Tables

Table 2.1 Minimum breakdown voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Table 2.2 Five kinds of models for investigation of different power networks . . . . . . . . . . . 15

Table 4.1 Numerical Parameters A and B of Townsend Coefficient α . . . . . . . . . . . . . . . . . .24

Table 4.2 Calculation Process of Air Breakdown Voltage (A=15 1/cm Torr,

B=365 V/cm Torr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

Table 4.3 Calculation Process of Nitrogen Breakdown Voltage (A=10 1/cm Torr,

B=310 V/cm Torr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Table 4.4 Calculation Process of Helium Breakdown Voltage (A=3 1/cm Torr,

B=34 V/cm Torr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Table 4.5 Calculation Process of Argon Breakdown Voltage (A=12 1/cm Torr,

B=180 V/cm Torr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..29

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List of Figures

Figure 2.1 Schematics of gas discharge process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Figure 2.2 Curve of current versus applied voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Figure 2.3 Paschen’s law for breakdown voltages of H2, Air and CO2 . . . . . . . . . . . . . . . . . . . . .10

Figure 2.4 Paschen’s curves of different gases under 400 Hz at room temperature . . . . . . . . . . 11

Figure 2.5 The development of avalanche to a streamer in a uniform field (+= positive ions,

-=electrons, ph= photons emitted from the avalanche . . . . . . . . . . . . . . . . . . . . . . . . .12

Figure 2.6 Ratio of high-frequency breakdown voltage to static breakdown

voltage as a function of frequency for a uniform air gap . . . . . . . . . . . . . . . . . . . . . . .14

Figure 2.7 The main processes responsible for the production of the charged

particles in a gas discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Figure 2.8 Schematic of triple junction in vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Figure 2.9 The mechanism of gas molecules are desorbed from the surface . . . . . . . . . . . . . . . .17

Figure 2.10 The needs for high power level space system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Figure 3.1 Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

Figure 3.2 The schematic of the experiment setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

Figure 3.3 Point-to-point electrode configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

Figure 4.1 Air Breakdown Voltage as a Function of Pressure with Theoretical Data . . . . . . . . 26

Figure 4.2 Nitrogen Breakdown Voltage as a Function of Pressure with Theoretical Data . . . 27

Figure 4.3 Helium Breakdown Voltage as a Function of Pressure with Theoretical Data . . . . .28

Figure 4.4 Argon Breakdown Voltage as a Function of Pressure with Theoretical Data . . . . . 29

Figure 4.5 Voltage (top), light emission (bottom) waveforms of a breakdown

event point-to-point electrode geometry for DC voltage at 100 milliTorr . . . . . . . . 30

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Figure 4.6 Voltage (top), light emission (bottom) waveforms of a breakdown event

point-to-point electrode geometry for DC voltage at 6 Torr . . . . . . . . . . . . . . . . . . . .31

Figure 4.7 Air Breakdown Voltage as a Function of Pressure with Experimental Data . . . . .32

Figure 4.8 Nitrogen Breakdown Voltage as a Function of Pressure with

Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

Figure 4.9 Helium Breakdown Voltage as a Function of Pressure with

Experimental Data (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

Figure 4.10 Helium Breakdown Voltage as a Function of Pressure with

Experimental Data (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

Figure 4.11 Argon Breakdown Voltage as a Function of Pressure with

Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

Figure 4.12 Comparison between Theoretical and Experimental Air Breakdown

Voltage Curve (Experimental top, Theoretical bottom) . . . . . . . . . . . . . . . . . . . . . . 35

Figure 4.13 Comparison between Theoretical and Experimental Nitrogen Breakdown


Figure 4.14 Comparison between Theoretical and Experimental Argon Breakdown


Figure 4.15 Comparison between Theoretical and Experimental Helium Breakdown

Voltage Curve (a) first time (b) second time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37

1

CHAPTER 1

INTRODUCTION

Modern electrical industry with high voltage levels, needs the investigation of breakdown

characteristics of dielectrics. Aerospace industry, such as aircraft and space station applications,

is also requiring much higher power levels nowadays. Switched-mode power supplies offer

solution to overcome these challenges. Meanwhile, understandings of the effects of higher

voltage levels on insulator breakdown under sub-atmospheric vacuum condition are essential.

The high voltage insulation becomes more and more important in power systems. In order

to reduce the losses on transmission lines, higher voltage levels are utilized in many countries.

Therefore, the development of high voltage insulation technologies determines the reliability

of power supply. Gaseous dielectrics, especially the air, have wide range of applications in

power system. Basic requirements for an ideal gaseous insulator are to be cheap, stable, and not

produce flammable or toxic materials under prolonged electrical stresses. It should also have

high uniform and non-uniform field dielectrics strengths under AC, DC and pulsed power [1].

Air, used as an insulator, is applied in most high-voltage transmission lines and open air

circuit-breakers. Under normal circumstances, the air is not conductive and known as an

insulator. On the other hand due to the cosmic rays, it normally contains a small amount of

charged particles, but the number is extremely low, unable to form a conductive path. However,

if the air gap is applied a critical voltage, the current in the air gap will suddenly surge, with

apparent light and heat phenomenon at the same time. Then it will suddenly lose insulating

properties and a conductive path will be formed. This phenomenon is called the gas discharge.

There are two forms of gas discharge, namely breakdown and flashover. The former refers to

2

the pure air gap discharge, and the latter refers to the gas discharge along a solid surface.

Breakdown and flashover are collectively referred as discharge. The gas discharge will only

cause a temporary loss of the insulation. Once the discharge is extinguished, it can recover

insulation performance, so the gas insulation has a kind of self-recovery insulation property.

Air is the cheapest and inexhaustible insulation material. Usually air is used in engineering as

the outer insulation of electric equipment and insulation of overhead transmission line, whose

breakdown strength is 30kV/cm. In the gas dielectric, in addition to air, large amounts of sulfur

hexafluoride are used as insulating medium; sulfur hexafluoride gas is often an internal

insulation for electrical equipment.

Compared with other dielectric materials, vacuum theoretically has the strongest dielectric

breakdown strength, because there is no residual gas and electron collision in the interelectrode

gap. According to Paschen’s Law, the sub-atmospheric pressure means much lower breakdown

voltage level than atmospheric environment. On the other hand, in vacuum, breakdown voltage

can be higher than the atmospheric pressures. In practice, there are absorbed gas and other

contaminants exist on the surface of metallic electrodes in vacuum environment. Generally, the

residual gas pressure of 10-9-10-12 bar exist in what is considered to be the vacuum environment,

and it is called “partial vacuum” environment. When certain threshold electric field intensity is

reached, electric field will stimulate charge carriers, and breakdown or flashover will occur

finally. However, with a suitable design, the vacuum breakdown strength is still better than

most of the dielectric materials. This is why vacuum insulation could be used widely in space

power systems. It’s also the necessity why we study the breakdown characteristics of materials

under vacuum condition.

With the advanced developments in aerospace technologies, higher power levels are

utilized to satisfy the increasing requirements. The International Space Station (ISS) is using a

160V operation voltage compared to a previous 28V standard voltage, and up to 100kW power

3

level. But more power means heavier power supply system. Generally, researchers use higher

frequency level and more compact components to match the requirements. But this, more

compact design brings some insulation failures due to the overstress, incompatible

coordination. Therefore, switch mode power supply (SMPS) becomes more favored because of

its advantages in compactness and effectiveness. The working frequency of high voltage SMPS

in space system is increased from a low range of 60 Hz ~ 400 Hz to radio frequency range of 10

kHz ~ 1 MHz. Thus, SMPS needs a high switching frequency during work. In space systems,

high frequency levels enhance the partial discharges and corona, resulting in power loss and

degradation, aging or even thermal breakdown of the bulk insulation and components. High

frequency also generates electromagnetic interference which disturbs the signal transmissions

in space power systems [11]. The dielectric surface composition and the surface charging are

affected by the low earth orbit (LEO) plasma and UV irradiation. Also, LEO plasma and UV

irradiation generate seed electrons for the breakdown process [2]. The insulation in ground

based systems already experience short circuiting, power losses, and impose spurious signals

onto communication systems and sensitive sensors due to arcing discharges. In space systems,

other environmental factors, in addition to the above failures, such as electrical degradation and

flashover at lower voltages might occur due to the molecular and particulate contaminants and

outgassing [11]. It is important to clarify the breakdown characteristics when the power supply

working with contaminations under such a high frequency operation.

Significantly, vacuum insulation is a well-known technology for space power systems.

But it is significantly important in pulsed power systems and has already been researched for

decades. The recent advances of large pulsed power devices enhance the necessity for

developing vacuum insulation technologies [3].

Also, the flashover voltage value of insulation is much lower than that of breakdown

voltage in vacuum. This is a significant constraint on development of more powerful and

4

compact pulsed power devices [10], because the power density transferred through

high-voltage systems is limited by the surface flashover across insulators [2]. This is the

starting point of continual surface flashover research in high voltage system insulation under

vacuum conditions [10].

Several unpredictable processes, such as partial discharges, corona and volume discharges

are detrimental to power systems and devices as they are the constant source of

electro-magnetic interference and energy loss. These processes could result in big problems as

insulation deterioration and component failure leading to bulk electrical breakdown.

Considering the components of power system, the most significant conditions are the geometry

of electrode gap (homogeneous, inhomogeneous), type of the field (polar, and unipolar fields),

the type of medium (electronegative, atomic, molecular, etc.), the amplitude of applied voltage,

and the operation pressure. The breakdown behavior in vacuum is still not clear completely,

even it has been extensively studied for decades. Systemic results about the breakdown

characteristics of some different gases are needed when DC voltage is applied [6]. Therefore,

this study focuses on the breakdown characteristics of gases under DC fields in partial vacuum

conditions.

The insulating materials influence the breakdown characteristics of total power system.

The most common and popular dielectrics are gases. These dielectrics play an important role in

many special high voltage areas. It is valuable to study electrical properties of gases, especially

under different conditions, such as the ionization, corona and breakdown process [1].

In recent decades, many researches focus on improving surface insulation strength through

doping other metal oxides such as alumina into epoxy. Therefore, high performance composite

insulation materials are produced to match more rigorous requirements [5]. The materials made

by adding nano-scale particulates into polymer based bulk are called nano-dielctrics. It has

been observed that these nano-scale particulates bring significant improvements on the thermal,

5

electrical and mechanical performances of polymeric materials. Besides, initial findings show

that the nano-composite materials have lower electrical conductivity and higher electrical

breakdown strength compared to the non-filler added polyamides, These properties make

nano-dielectric materials prime candidates for electrical insulation for multi-stress and high

repetition rate (high frequency operation) for compact and/or high voltage/power electrical

systems.

Insulating materials can be used for both insulation purposes and for charge storage, in

addition to other purposes like heat conduction (as in liquids) and mechanical support (as in

solids), which make them play a significant role in the design and performance of high voltage

power systems [4].

6

CHAPTER 2

BACKGROUND AND LITERATURE

2.1 Basic concepts

Breakdown processes have been studied over many decades. There are several important

concepts contribute to the formation of breakdown in air. Primary electrons are usually trapped

in air, but they will be released by cosmic rays, and background radiation, to collide with

neutral molecules after accelerating by strong electrical field. This ionization process is

cumulative and promotes the formation of avalanche of electrons, when electrons get enough

energy to cause ionization of the background gas. More details about this process will be

introduced in next section [17].

2.2 Gas Breakdown mechanisms

2.2.1 Townsend discharge theory

The Townsend theory is the earliest theory to explain the breakdown and the gas discharge

mechanism. As shown in the Fig. 2.1, two parallel-plate electrodes connected with the positive

and negative polarities of DC voltage source respectively, forms a uniform electrical field

between them. The free electrons within the gap can be accelerated by the electrical field.

They can also be released from the cathode, and collide with the gas molecules to generate

more electrons. These electrons are also collide with gas molecules and generate more

electrons. Finally, avalanche phenomenon is formed and an electrical conducting pathway

through the gas is established. But the electrical field strength and mean free path are important

for this discharge process. The electrons must acquire sufficient energy from the applied field.

If the electrical field is too small, the electron will not acquire enough velocity to collide with

other gas molecule. If the mean free path is too long, the electron will reach anode without

7

colliding with other gas molecules. On the other hand, if the mean free path is too short, the

electrons will lose their accelerated energy in a series non-ionizing collisions.

Figure 2.1 Schematics of gas discharge process

The relationship between the current and the applied voltage is shown in Figure 2.2. At the

beginning, the current is proportional to the applied voltage closely. After that, there is a

saturation stage, the current will reach I0 for a while. After passing this saturation stage, the

current will increase exponentially.

Figure 2.2 Curve of current versus applied voltage

8

The average number of electrons released by a positive ion is given by

0

e

1 e 1)

d

d

I

I

(2.1)

Where I is current flowing in the circuit, I0 is saturation current, ɑ is first Townsend coefficient,

γ is Townsend secondary ionization coefficient, d is distance between electrodes. Neglecting

the power supply internal resistance, the current becomes infinite if

1( )1de (2.2)

Normally, eαd >> 1, and Equation (2.2) is simply expressed as

1de (2.3)

2.2.2 Paschen’s law

The Paschen’s law essentially describes the breakdown characteristic of a gas in a gap is a

nonlinear function of the product of the gas pressure, p, and the gap distance, d, and usually

written as V= f (pd). Actually, the pressure should probably be replaced by the gas density. It

has been shown that the gas breakdown criterion is given as γ (eαd-1) =1. The coefficients of α

and γ can be determined as functions of the gas pressure p and the electric field E.

For parallel plate electrodes E = V/d, γ = f1 (E/p) and α = pf 2(E/p). Thus, rewriting

Equation (2.2) we have

1 /

1

( )/ 1 1pd f V pdf V pd e (2.4)

With understanding the nature of functions f1 and f2, the Equation (2.2) shows a

relationship between breakdown voltage and product pd, and can be rewrite as,

V F pd (2.5)

9

This equation is very important for high voltage engineering. It is known as the Paschen’s

law, and has been experimentally measured for many gas. At low pd values the breakdown

voltage is inversely proportional to the pd value, and at high pd values it is directly proportional

to the pd parameter. There is a range where breakdown voltage reaches a minimum and it is

called the Paschen minimum. These minimum breakdown voltages for different gases are

showed in Table 2.1.

Table 2.1 Minimum breakdown voltages

Gas Vs min (V) Pd at Vs min (Torr-cm)

Air 327 0.567

Argon 137 0.9

H2 273 1.15

Helium 156 4.0

CO2 420 0.51

N2 251 0.67

N2O 418 0.5

O2 450 0.7

SO2 457 0.33

H2S 414 0.6

Paschen’s curves for three gases, H2, Air and CO2 are shown in Figure 2.3. These curves

states that the relationship between breakdown voltages and product pd are not linear and all

have a minimum value breakdown voltage corresponding to a (pd)min value. The approximate

pd value for air equals to 5 Torr-cm. If the pd< (pd)min, electrons crossing the gap made only

few collisions and higher voltage are needed to supply sufficient energy to the electrons to

cause breakdown. When pd>(pd)min, there are more frequent collisions between electrons and

gas molecule than at (pd)min, but electrons gain lower energy between collision, and the

breakdown voltage for these conditions becomes higher than that of at (pd)min values.

10

Figure 2.3 Paschen’s law for breakdown voltages of H2, Air and CO2

Traditional aerospace system employ 400Hz frequency because the low frequency of

switched frequency. Figure 2.4 shows the Paschen’s curve at 400 Hz. Currently, the frequency

in space systems is much higher than before, and Paschen’s law still can be observed in kHz

frequency system.

11

Figure 2.4 Paschen’s curves of different gases under 400 Hz at room temperature [18]

2.2.3 Streamer Theory of Breakdown

Paschen’s law has introduced the importance of pd in the breakdown process. The

branched path and zigzag channel cannot be explained by Townsend theory under large pd

values. In this case, streamer theory is presented to interpret these questions. The streamer

process is shown in Figure 2.5.

Slow moving positive ions and fast moving electrons are generated when the electron

avalanche happens. Positive ions are left behind; meanwhile electrons accumulate at the anode

area. Atoms are excited by this primary avalanche and release photons in the gap. These

photons are absorbed by the gas atoms at different places. This process produces ionization and

photoelectrons (See Figure 2.5 a) and therefore generates the auxiliary avalanche.

The auxiliary avalanche, as the second avalanche, repeats above process and generates

more photons and photoelectrons within the gap (See Figure 2.5 b). This stimulates more

12

auxiliary avalanches in coming period. But the space charge formed during this process distort

the electrical field and simultaneous auxiliary avalanches form a zigzag patters from tip to tail

(See Figure 2.5 c). With the developing of the avalanches, the spark channels are formed that

connect the anode and cathode.

Figure 2.5 The development of avalanche to a streamer in a uniform field (+= positive ions, - =

electrons, ph= photons emitted from the avalanche [1]

2.3 High Frequency Breakdown

The discharge behavior becomes different as the frequency of the applied field reaches a

relative high level. The maximum distance Lmax lets all positive ions travel during a half-cycle

of the applied is expressed as,

1/2

max0

sin 2f k VV

L k ftdtd fd

(2.6)

13

Where V is the maximum amplitude of the applied voltage, d is the gap distance, and V/d sin

(2πft) is the field strength. In this case, when d > Lmax, no positive ion cannot reach the opposite

electrode during the half-cycle of the field. Then the Equation (2.6) can be revised to get a

critical frequency fc,

2c

kf V

d

(2.7)

When f < fc, the breakdown characteristics is similar to statics field. When f > fc, the

positive ions will have no time to reach the cathode and oscillate in the gap. This accumulative

charge will distort the field, increase the density of ions until avalanches happen. Due to the

different mechanism, the breakdown under high frequency AC will occur at lower field

strength than that under DC. This phenomenon are shown in Figure 2.6. Before positive ion

oscillation, high frequency breakdown voltage is the same as under statics field. After that, the

breakdown curve drops because of the field distortion until electron oscillation starts. Electrons

will also not reach the anode during the half-cycle just like positive ions will not be able to get

the cathode. Electrons oscillate between the electrodes to neutralize the positive ions and

electrical field. This feature of breakdown forms the parabolic shape with increasing frequency

[16].

14

Figure 2.6 Ratio of high-frequency breakdown voltage to static breakdown voltage as a

function of frequency for a uniform air gap [16]

2.4 Air and Gas dielectrics Insulation

2.4.1 Air Insulation Application

Due to the excellent insulating properties, air is mostly used as outdoor high voltage power

system applications as well as insulation for indoor power systems. According to the practical

applications in power system, air is often used to provide insulation protection for phase to

phase as well as phase to ground. Therefore, different models are designed to simulate these

different conditions. Table 2.2 summaries five kinds of commonly used models for power

system insulation [1].

15

Table 2.2 Five kinds of models for investigation of different power networks [1]

Network section Function Model used for simulation

Phase to phase insulation To provide insulation

between two phases of an

AC transmission line or

between opposite poles of a

bipolar DC line

Conductor- conductor, i.e.,

parallel cylinders or rod-

plane electrodes to

simulate the worst case of a

sharp point on one

conductor opposite to the

other conductor

Phase to tower or phase to

ground insulation

To provide insulation

between the phase

conductor and the

grounded tower or the

ground itself

Conductor- plane or rod-

plane electrodes.

Small diameter conductor

to grounded object

insulation

To provide insulation

between a sharp conductor

and a flat grounded objet in

front of it. This type of

geometry has the lowest air

breakdown strength

Point- plane or rod- plane

electrodes

Sphere-sphere gaps High voltage

measurements and high

voltage switches in impulse

generators

Sphere-sphere electrodes

High voltage protective or

measuring gaps

To bypass high voltage

surges to ground by a spark

discharge. Also used for

impulse chopping and for

high direct voltage

measurements

Rod-rod electrodes

2.4.2 Gas Dielectrics

Due to the excellent properties of compactness, restorability and light weight, gases are

widely utilized in space system and power system insulation. Each gas has a breakdown

voltage at a specific pressure, temperature, and other parameters. Breakdown voltage is defined

as the peak applied voltage across the electrodes when breakdown phenomenon occurs or spark

channel forms. When DC voltage is applied across the electrodes, charged particles may be

produced within the gap (see Figure 2.7). Such charged particles may include, electrons ( e- ),

positive ions ( A+ )and negative ion ( A- ).

16

Figure 2.7 The main processes responsible for the production of the charged particles in a gas

discharge

2.4.3 Vacuum Surface Flashover

Triple junction is an important mechanism for solid insulation surface flashover in vacuum.

As shown in Figure 2.8, the junction part, the cathode metal, vacuum and solid insulator, is the

most vulnerable part because of the different insulating properties of these materials, as well as

the field enhancement at the junction. Emission of a single electron from the cathode tip as the

initial electron, collides with the surface of the insulator to generate another electron. The

initial and the secondary electrons continue to hit the dielectric surface, leading to an electron

cascade and form an electron avalanche finally. This is the simple introduction to secondary

electron emission avalanche (SEEA). When the electron flow reach the anode, the surface

flashover will be completed.

Charged particles production in gas discharge

A- e- and A+ e-

In gas medium At cathode surface In gas medium

Attachment

Ion-pair production

Photoionization

Field emission

Electron impact

+ve ion bombardment

Thermal ionization

Photoionization

Impact ionization

17

Figure 2.8 Schematic of triple junction in vacuum

The classical interpretation assumes that the intermediate stage of surface flashover is an

electron cascade, and the final stage occurs in desorbed surface gas or in vaporized insulator

material. The electron cascade can strongly affect the future development of SEEA.

Figure 2.9 The mechanism of gas molecules are desorbed from the surface

Electron bombardment desorbs adsorbed gas which is ionized by the electrons (See Figure

2.9). Some positive ions drift toward the cathode. This process enhances the electrical field E.

The enhanced electrical field will increase electron emissions from the triple junction further

18

and increase the current along the insulator surface. In this model, desorption of adsorbed gas is

a key process leading to the surface flashover of an insulator.

2.5 Space System Insulation

Nowadays, space system needs high voltage and HV insulation (see Figure 2.10). In

practice, the space environment is highly variable and anything but empty. Therefore, we need

to consider many influences, such as residual gas, contamination, and etc. The most serious

factors influencing electrical phenomena are the local radiation environment, thermal cycling,

and local plasma density, neutral particle density, out gassing /effluents, and the meteoroid flux.

In this thesis, only the breakdown of several gases at subatmospheric pressure, where most

aerospace vehicles operate, is studied. Other space environmental effects are not studied.

Figure 2.10 The needs for high power level space system

Demand for higher

power level

Joule heating

increases

Current high

Keep safe voltage

More massive

electrical conductor

Less payload or more

cost

19

CHAPTER 3

EXPERIMENTAL SETUP AND PROCEDURE

3.1 Experimental Setup

The vacuum chamber is the main body of the experimental set-up (see Figure 3.1). The

High Voltage (HV) probe, the current probe and the Photomultiplier (PMT) are connected to

the experiment through different ports. HV probe is Tektronix p6015, to monitor the voltage

inside the chamber. A Pearson Coil is used as the current probe, and encircle the wire that is

connected to the anode in the chamber. The light emission from the plasma generated at

breakdown is monitored by a Hamamatsu PMT. The current from the PMT is converted to

voltage utilizing a Keithley 485 pico-ammeter. The light emission strength and voltage

waveforms are display on the screen of an Agilent DSOX2012A digital oscilloscope (see

Figure 3.2).

The light emission captured by PMT is used as the trigger signal to capture the breakdown

voltage for the experiments. This is more reliable than the discharge current or negative slope

of breakdown voltage. Therefore, shading the chamber form the outside light is necessary to

avoid the influence of external light source on the PMT signal.

As we known, the breakdown phenomenon occurs instantaneously. Once the breakdown

occurs, the oscilloscope will captured light emission strength and breakdown voltage data

simultaneously.

20

Figure 3.1 Vacuum Chamber

The point to point electrode geometry is one of the simplest configurations. As mentioned

before, it is used to simulate phase-to-phase breakdown condition. The experimental set us

consists of two needle-shape stainless steel electrodes that are placed 1 cm apart from each

other as seen in Figure 3.3.

21

Vacuum ChamberCurrent

Probe

Voltage Probe

PMT

ElectrometerOscilloscope

Anode

Cathode

Figure 3.2 The schematic of the experiment setup

22

Figure 3.3 Point-to-point electrode configuration

23

3.2 Experimental Procedure

The experiments focus on the gas breakdown phenomenon. The breakdown voltage

waveform data are recorded by the oscilloscope for each pressure then a set of data is generated

as the breakdown voltage versus pressure. The experiments are conducted under partial

vacuum environment, mainly at the range of 100 milliTorr to 10 Torr. Before every set of

experiments, it is necessary to bump the chamber until the chamber pressure is below 100

milliTorr, then fill in the corresponding gas to satisfy the pressure requirement. In the pressure

sweep experiments, at a constant pressure, the DC voltage is applied between the electrodes

and increased at a constant rate (about 100V/s) from 0 volts to until the breakdown occurs. The

pressure ranges are from minimum level of 100 milliTorr to different upper pressure level. Air

and Nitrogen are common gases, therefore their experimental pressure range will be 100

milliTorr to 2 Torr. The experiments with argon gas is under 100 milliTorr to 5 Torr. But

Helium being the second lightest element in nature, therefore, pumping the chamber down to

vacuum level and refilling at each fixed pressure value is necessary to record correct

breakdown data. Also, it is know that the Paschean minimum occurs at about 5 too-cm, the

upper pressure for helium breakdown experiments reaches 10 Torr. For every fixed pressure

value of each gas, four breakdown data points are acquired. The average value of these

repeated data reduces the error effectively.

24

CHAPTER 4

RESULTS AND DISCUSSION

4.1 Theoretical Calculation

The experiments are the primary stage of understanding the high-voltage insulation. It is

important to understand the meaning of Townsend theory and Paschen’s law. According to

these two significant theories, we can get the theoretical calculation results to plot the

breakdown voltage curve versus pressure of gases. Every curve should have its own Paschen

curve and (pd)min point. This theoretical curve will be the reference for the real experimental

result.

Reviewing the content mentioned in Chapter 2, the equations can be rewrite as:

/

BAexp

p E p

（4.1）

Where α is the Townsend coefficient, p is the pressure and E is the electrical field. A and B are

specific constants and given in Table 3.1 for each gas studied.

Table 4.1 Numerical Parameters A and B of Townsend Coefficient α

Gas A, 1/cm Torr B, V/cm Torr

Air 15 365

N2 10 310

He 3 34

Ar 12 180

The breakdown voltage as a function of the important parameter pd:

B pdV

C ln pd

(4.2)

25

B is provided by Table 31, and is given by C= ln A- ln ln (1+1/γ).

It is convenient to calculate the breakdown voltage if the Townsend secondary ionization

coefficient γ is known. Townsend secondary ionization coefficient γ depend on type of gas,

cathode material, and reduced electrical field E/p. This value of γ is measurable, but varies

for different materials and gases. Typical range of γ is 0.01~0.1 [19]. We select γ=0.1 for this

calculation. Thus, it is enough to calculate all the breakdown voltages as follows below and

shown in Figure 4.1. With the data of Figure 4.1, a Paschen curve can be plotted.

One important point needed to notice is that the values of A and B are empirical, based on

many stable previous studies. But they are valid only between 1-10 Torr approximately.

Because the Townsend breakdown theory is mainly focus on glow charge and is valid in this

pressure range. The theory breakdowns at pressure below 100 milliTorr. That is exactly the

reason for negative values in the charts (figure 4.1). These negative values will be neglected

during plotting the Paschen curves.

Figure 4.1, 4.2, 4.3, and 4.4 show the calculations of breakdown voltages of air, nitrogen,

helium, and argon respectively. In the valid pressure range, all figures show a good match

with well-known Paschen curve.

26

Table 4.2 Calculation Process of Air Breakdown Voltage (A=15 1/cm Torr, B=365 V/cm Torr)

pd(Torr cm) d(cm) γ C Air Breakdown Voltage (V)

0.13 1 0.1 1.833459 -229.491

0.15 1 0.1 1.833459 -860.022

0.2 1 0.1 1.833459 325.8624

0.3 1 0.1 1.833459 173.9514

0.4 1 0.1 1.833459 159.1857

0.5 1 0.1 1.833459 160.044

0.6 1 0.1 1.833459 165.5788

0.8 1 0.1 1.833459 181.331

1 1 0.1 1.833459 199.0773

2 1 0.1 1.833459 288.9251

3 1 0.1 1.833459 373.4562

4 1 0.1 1.833459 453.4509

6 1 0.1 1.833459 604.1016

8 1 0.1 1.833459 746.2495

10 1 0.1 1.833459 882.4858

15 1 0.1 1.833459 1205.546

20 1 0.1 1.833459 1511.64

Figure 4.1 Air Breakdown Voltage as a Function of Pressure with Theoretical Data

0

200

400

600

800

1000

1200

1400

1600

0.1 1 10 100

Bre

akd

ow

n V

olt

age

(V

olt

s)

Pressure × Gap Distance (Torr· cm)

27

Table 4.3 Calculation Process of Nitrogen Breakdown Voltage (A=10 1/cm Torr, B=310 V/cm

Torr)

pd(Torr cm) d(cm) γ C Nitrogen Breakdown Voltage (V)

0.01 1 0.1 1.427994 -0.97571

0.26 1 0.1 1.427994 996.0447

0.27 1 0.1 1.427994 705.3744

0.3 1 0.1 1.427994 415.1398

0.4 1 0.1 1.427994 242.3281

0.5 1 0.1 1.427994 210.9284

0.6 1 0.1 1.427994 202.7982

0.8 1 0.1 1.427994 205.8347

1 1 0.1 1.427994 217.0878

2 1 0.1 1.427994 292.2955

3 1 0.1 1.427994 368.0827

4 1 0.1 1.427994 440.6088

6 1 0.1 1.427994 577.684

8 1 0.1 1.427994 707.0694

10 1 0.1 1.427994 830.9702

15 1 0.1 1.427994 1124.263

20 1 0.1 1.427994 1401.533

Figure 4.2 Nitrogen Breakdown Voltage as a Function of Pressure with Theoretical Data

0

200

400

600

800

1000

1200

1400

1600

0.1 1 10 100

Bre

akd

ow

n V

olt

age

(V

olt

s)


28

Table 4.4 Calculation Process of Helium Breakdown Voltage (A=3 1/cm Torr, B=34 V/cm

Torr)

pd(Torr cm) d(cm) γ C Helium Breakdown Voltage (V)

0.01 1 0.1 0.224021 -0.06752

0.1 1 0.1 0.224021 -1.24391

0.2 1 0.1 0.224021 -3.33307

0.3 1 0.1 0.224021 -6.23968

0.4 1 0.1 0.224021 -10.0964

0.65 1 0.1 0.224021 -25.6527

0.7 1 0.1 0.224021 -30.226

0.8 1 0.1 0.224021 -41.5985

1 1 0.1 0.224021 -78.9365

2 1 0.1 0.224021 259.1251

3 1 0.1 0.224021 152.7205

4 1 0.1 0.224021 142.3236

6 1 0.1 0.224021 149.8861

8 1 0.1 0.224021 164.9769

10 1 0.1 0.224021 181.6376

15 1 0.1 0.224021 223.947

20 1 0.1 0.224021 265.1065

Figure 4.3Helium Breakdown Voltage as a Function of Pressure with Theoretical Data

0

50

100

150

200

250

0.1 1 10 100

Bre

akd

ow

n V

olt

age

(V

olt

s)


29

Table 4.5 Calculation Process of Argon Breakdown Voltage (A=12 1/cm Torr, B=180 V/cm

Torr)

pd(Torr cm) d(cm) γ C Argon Breakdown Voltage (V)

0.16 1 0.1 0.955569 -129.574

0.17 1 0.1 0.955569 -189.308

0.2 1 0.1 0.955569 41032.45

0.3 1 0.1 0.955569 132.8928

0.4 1 0.1 0.955569 103.7427

0.5 1 0.1 0.955569 98.12814

0.6 1 0.1 0.955569 98.22739

0.8 1 0.1 0.955569 103.8083

1 1 0.1 0.955569 111.7794

2 1 0.1 0.955569 156.2865

3 1 0.1 0.955569 199.3409

4 1 0.1 0.955569 240.2715

6 1 0.1 0.955569 317.4533

8 1 0.1 0.955569 390.2696

10 1 0.1 0.955569 460.0168

15 1 0.1 0.955569 625.2366

20 1 0.1 0.955569 781.5812

Figure 4.4 Argon Breakdown Voltage as a Function of Pressure with Theoretical Data

0

100

200

300

400

500

600

700

800

900

0.1 1 10 100

Bre

akd

ow

n V

olt

age

(V

olt

s)


30

4.2 DC Breakdown Experiments

As described in Chapter 3, DC voltage is applied across the electrodes, increased

gradually with a rate of 100 V/s, until the breakdown phenomenon occurred. The plasma

initiation light emission is recorded by the PMT (shown in Figure 4.5 yellow bottom line).

The acquisition system triggered by positive slope edge of light signal and used to capture the

breakdown voltage signal. Therefore, these two signals displayed on the screen. In order to

decrease the errors, the experiments under same pressure was repeated four times. The

average value of these four data is the breakdown voltage for its corresponding pressure.

Similar experiments were conducted in air, nitrogen, helium, and argon. Specially, in the

experiments of helium, because its property of light mass, it is necessary to pump the

chamber down at the beginning of every pressure. Even though, satisfactory data cannot be

obtained easily. Therefore, a second set of helium breakdown voltage experiments was

conducted to ensure the accuracy of first set of data.

Figure 4.5 Voltage (top), light emission (bottom) waveforms of a breakdown event point-to-

-point electrode geometry for DC voltage at 100 milliTorr

31

Figure 4.6 Voltage (top), light emission (bottom) waveforms of a breakdown event point-to-

-point electrode geometry for DC voltage at 6 Torr

Figure 4.7 shows the air breakdown voltage curve. This is a right hand side of the Paschen

curve with obvious rising up tendency. Its pdmin appears at 100~200 milliTorr. If extend the left

part of this curve to far less than 100 milliTorr, it should have a significant high breakdown

voltage value. Between the range of 100 miiliTorr to several Torr, air has an excellent

insulating property, its lowest breakdown voltage is still more than 640 V.

Figure 4.8 shows the nitrogen breakdown voltage curve. Its breakdown curve resembles the

Paschen curve with both positive and negative slope. Although the values at 400 and 600

Torr·cm distort the bottom part of this curve, it is still complete and a good curve to show the

insulating properties in this range.

Figure 4.9 (a) has two seems to be in error at 2.4 Torr and 3 Torr. Because of the special

properties of helium, the breakdown voltage values from 1 Torr to 8 Torr fluctuate at a stable

32

region. Only if the pd reach to more than 10 Torr, the breakdown voltage could have a rising up

tendency. Because of the limitation of pressure gauge, the voltage at more than 10 Torr was not

measured in this experiment. The curve of Figure 4.9 (b) is similar to Figure 4.9 (a). That

means no severe error occur in our experiments and the overall shape of curve is correct.

Figure 4.10 shows the argon breakdown voltage curve. It has a good configuration of curve.

Its pdmin is about 800 ~1000 miliiTorr, which is match the pdmin provided by Table 2.1.

Figure 4.7 Air Breakdown Voltage as a Function of Pressure with Experimental Data

Figure 4.8 Nitrogen Breakdown Voltage as a Function of Pressure with Experimental Data

33

Figure 4.9 Helium Breakdown Voltage as a Function of Pressure with Experimental Data (a)

Figure 4.10 Helium Breakdown Voltage as a Function of Pressure with Experimental Data (b)

34

Figure 4.11 Argon Breakdown Voltage as a Function of Pressure with Experimental Data

4.3 Comparison between Theoretical and Experimental Curves

Figures 4.12, 4.13, 4.14, and 4.15 show the comparison of theoretical and experimental

breakdown voltages of air, nitrogen, argon, and helium respectively. Compared to the

experimental curve with theoretical curve in the same coordinate system, these two curves

have same tendency at most pd point, but with a constant shift in voltage values. That is

because the theoretical curve are based on the uniform electrical field, the γ and value of A and

B are constant under the prediction of uniform electrical field. But the point-to-point electrodes

have only nonuniform electrical field. It seems like reasonable to have a constant difference

value. The detail reason for this phenomenon need future research in the future.

35

Figure 4.12 Comparison between Theoretical and Experimental Air Breakdown Voltage Curve

(Experimental top, Theoretical bottom)

Figure 4.13 Comparison between Theoretical and Experimental Nitrogen Breakdown Voltage

Curve (Experimental top, Theoretical bottom)

36

Figure 4.14 Comparison between Theoretical and Experimental Argon Breakdown Voltage

Curve (Experimental top, Theoretical bottom)

37

(a)

(b)

Figure 4.15 Comparison between Theoretical and Experimental Helium Breakdown Voltage

Curve (a) first time (b) second time

38

4.4 Summary

This study I introduced the method to calculate the breakdown voltages for four gases with

Paschen’s law and Townsend theory. Then the experimental study is conducted confirming the

correctness of our calculation under DC applied voltage.

Theoretical calculation is based on Townsend secondary ionization coefficient γ, which

depends on the type of gas, cathode material, and reduced electrical field E/p. This value of γ

is set at 0.1 in this calculations for all four different gases. The breakdown voltage is a

function of pressure under DC voltage. They also have a parabolic curve like Paschen curve

without the influence of error data.

Experiments confirms the existence Paschen curve between 100 milliTorr and several

Torr. It also shows the breakdown voltage is a function of pressure. Because the difference of

applied electrical field, uniform electrical field for theoretical and nonuniform one for

experimental, theoretical and experimental breakdown voltage curves have same tendency at

most pd point, but with a constant shifted voltage value. The experiments are successful to

confirm the consistency between theoretical and experimental breakdown voltage curves.

39

CHAPTER 5

CONCLUSIONS

This thesis is mainly consist of two parts, one is theoretical calculation, and the other one is

experimental confirmation. It clarifies the correlation between two different research methods

for gas breakdown phenomenon study. Gaseous dielectrics is the simplest insulation material

for power system. Study with gas dielectrics is also the initial stage and necessary way to

research on solid dielectrics. Familiar with the basic breakdown mechanism is benefit for

learning with plasma and micro- or nanodielectrics. This experiment utilized point-to-point

electrode, to simulate conditions of high voltage protective or measuring gaps.

In the first part, this theoretical calculation is based on Townsend breakdown theory and

utilized the secondary ionization coefficient γ, which depends on type of gas, cathode material,

and reduced electrical field E/p. It is convenient to calculate the breakdown voltage if we know

the Townsend secondary ionization coefficient γ for the gases in our experiments. But for the

sake of calculating an acceptable set of data, we set γ equal to 0.1 for all four gases in this

experiment. With the data of calculation, a Paschen curve can be drawn out easily. The values

of A and B used for calculation are empirical, based on many stable previous studies and are

valid only between 1-10 Torr approximately (glow discharge region). Before plotting the

breakdown voltages versus pressure curve, negative voltage values were deleted and removed

from the calculations. Finally, from the figures of theoretical calculation, it can be realized that

the breakdown voltage is a function of pressure under DC voltage. These figures own a

parabolic curve like Paschen curve when neglect the influence of error data.

40

As the second part of this thesis is the experimental study of breakdown of gases to

confirm the existence Paschen curve between 100 milliTorr and several Torr. It also shows

the breakdown voltage is a function of pressure. Because the difference of applied electrical

field, uniform electrical field for theoretical and nonuniform one for experimental, theoretical

and experimental breakdown voltage curves have same tendency at most pd point, but with a

constant difference value. The experiments successfully confirm the consistency between

theoretical and experimental breakdown voltage curves. Besides, the nitrogen and argon have

perfect Paschen curve in this pressure range under DC applied voltage. Nitrogen and air have

the largest breakdown voltage value at their pdmin. It is worth mentioning that their pdmin appear

at what the supposed to be. Conduction and ground are important prospects for this experiment.

Without stable wire conduction, flashover phenomenon occurred between two wires rather

than at the gap of two electrodes. We have tried copper wire, stainless steel wire until Teflon

wire is utilized in this experiment. Also, bad connection to absolute ground will lead to the

reference potential inaccuracy.

41

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